Cycling, twisting, and sewing in the group theoretic approach to strings (Q1122673)

This paper is a continuation of the authors' series of papers studying the action of the conformal group on the vertex operators of string theory [see ibid. 114, 613-643 (1988; see the preceding review Zbl 0676.22014) and the references there]. It is shown that cyclic permutations of the Koba-Nielsen variables are implemented by elements of the conformal group which can be interpreted geometrically as translations on the Riemannian surface which forms the world sheet of the string. The vertex operators also satisfy certain compatibility conditions corresponding to transport around homologically non-trivial closed loops on the surface. The authors ``also demonstrate that twisting and sewing, i.e. factorization, are an inevitable consequence of the method. We show that there exists a particularly simple choice of cycling transformations that leads to very great simplifications in the result for excited string scattering.''